Fawkes (D's phoenix) tries to alert Dumbledore to the "not serious" prisoner, for reasons that are not immediately clear.
Fawkes probably wants to help all the prisoners. That's what phoenixes do, they act as anti-Dementors of sorts. Dumbledore probably dismissed it as just the phoenix picking up on the prisoner's distress.
Dumbledore notes to Amelia Bones that there was an item hidden under a piece of cloth in Bellatrix's cell, which he was leaving to the forensic aurors to investigate
We saw Quirrel put this there (and Harry saw him too). What could this item be? Any unexpected item would ruin the death-doll pretense.
My guess: a vial with traces of poison to make it look like someone sneaked in poison for Bella and she drank it. ETA: but we don't know why Quirrel would do that; see discussion below.
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Again, test not interview. Their GPA is an average measure of maybe thousands of such simple problems - probably on average more rigorously produced, presented, and corrected than your problem presented in the interview.
Deciding based on a test in person instead of deciding on a number that represents thousands of such individual tests smacks of anecdotal decision-making.
Unfortunately, GPAs can lie. You cannot be certain of the quality of the problems and evaluation that was averaged to produce the GPA. So running your own test of known difficulty works well to verify what you see on the resume.
For example, I have to hire programmers. We give all incoming programmers a few relatively easy programming problems as part of the interview process because we've found that no matter what the resume says, it's possible that they actually do not know how to program.
Good resume + good interview result is a much stronger indicator than good resume alone.